Ok, you've just started your game, you've gotten your pokeballs, and are on your way to the first badge. You are suddenly attacked by a wild pokemon, and it's shiny! You successfully catch it and you feel whatever you would feel if you caught one.
Now the question comes. If you already had a planned-out team of pokemon you wanted, would you rearrange it to make room for your super-lucky catch?
For me, I would, and have. Because of two very lucky catches, my FR hall of fame included a shiny Pidgeot and Gengar.